He said that United Nations members remain unanimously committed to the denuclearization of the Korean Peninsula.

“We are not looking to the total annihilation of a country, namely North Korea, but as I said, we have many options to do so,” Mattis said.

While triggering global geopolitical shockwaves, North Korea's nuclear test also represents a flagrant personal challenge to President Donald Trump, and his strategy of escalating the showdown with Pyongyang with explosive rhetoric.

With his previous threat to rain "fire and fury" on North Korea and warning that the US military is "locked and loaded" to respond to Kim Jong Un's provocations, Trump set up a test of wills with his unpredictable adversary.

Now, with his nation's most powerful nuclear detonation Sunday, and a string of missile launches, including one over Japan, Kim has effectively called the President's bluff, escalating a dangerous foreign policy crisis.

Trump's options to prevent North Korea twinning a nuclear device with an intercontinental ballistic missile that could reach the US are narrowing, and with each North Korean move, the time available to act is running out.

Every time that the Trump administration has hiked pressure and rhetoric against Pyongyang, through sanctions, condemnations and military maneuvers and exercises, Kim has upped the ante in its showdown with Trump.

In this, the Trump administration is not alone — nothing the previous three US administrations did to halt North Korea's nuclear program worked either — with the isolated state on an arc to building a deliverable nuclear device.

Personal element

Those who support Trump's bombastic rhetoric say that since sanctions and pressure and diplomacy have in the past failed to slow North Korea's nuclear and missile program, the president's approach is worth a try.

But Trump has injected a particularly personal note into his confrontation with Kim, putting his own personal authority and credibility on the line, in a way that worries some national security experts.

Former CIA and National Security Agency director Michael Hayden told CNN's Dana Bash on "State of the Union" Sunday that he believed that Trump's national security team had framed a coherent policy on North Korea, especially in its effort to impress upon the Chinese the urgent need to use more of its influence to change North Korea's behavior.

But he said that the approach had sometimes been "inartfully executed" and warned that the president should avoid being drawn in to a mano-a-mano showdown with Kim in the wake of the nuclear test.

"I fear two things. The stray electron, the tweet that just goes out a 5 a.m. and unintentionally creates effects that make this go to a place where we don't want it to go," Hayden said. "The other one is this. We just got into a duel with the North Korean chairman, with Kim Jong Un. If we had a choice of weapons, I think it was a bad choice to get into a hyperbole contest with that kind of guy."

"Mr. President, this is not a manhood issue, this is a national security issue. Don't let your pride get ahead of wise policy here," he added.

Authority on the line

While putting Trump's authority on the line, Sunday's test also posed a challenge for the administration's sometimes confusing North Korea strategy, which has oscillated between Trump's threats and warnings that talks with Pyongyang won't work and his Secretary of State Rex Tillerson's assurances that dialogue is possible.

It has long been conventional wisdom that military action to destroy North Korea's nuclear capability is all but unthinkable because Pyongyang could send thousands of rockets across the demilitarized zone between the Koreas in reprisal, inflicting huge civilian casualties within a matter of minutes.

Trump's former political adviser Steve Bannon said in an interview with the American Prospect magazine last month that "there is no military solution" until someone solves the equation that suggests "10 million people" in Seoul could die under a North Korean onslaught.

But the White House has insisted that all options, including military ones are on the table. And Trump has given the impression that he might ultimately decide on a military strike either for strategic purposes or because he sincerely believes such a move is viable.

Asked Sunday if he would attack North Korea, Trump responded, "we'll see," as he left a church service near the White House.

The alternative would be for the president to accept the reality of a regime as unpredictable as that in Pyongyang having the capacity to hit the US with a nuclear weapon, and to put his faith in traditional doctrines of deterrence.

'Rogue nation'

On Sunday, Trump reacted to North Korea's claimed explosion of a hydrogen bomb by blasting the isolated state as a "rogue nation" that was "hostile and dangerous" to the United States.

But he also lashed out—at America's crucial ally South Korea.

"South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!" Trump tweeted.

South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!

The tweet came two days after a telephone conversation between Trump and South Korean President Moon Jae-in, and suggests that the call did not end with both leaders in firm agreement on the strategy going forward.

Trump's tweet also appears to validate one of Pyongyang's likely goals in continuing its nuclear and ballistic missile tests, driving a wedge between the United States and its allies as they respond to its actions.

Trump's rebuke of Moon also followed a Washington Post report on Saturday that he had instructed his aides to withdraw from a free trade pact with Seoul, a move that would severely strain ties with South Korea at an inopportune time.

Arizona Sen. Jeff Flake, a Republican, told Bash on "State of the Union" that pulling out of the deal would not be a good step at any time and "now is particularly troubling, given what South Korea is faced with."

The test will also renew tensions between China and the United States on how best to handle North Korea.

In his series of tweets the President noted that the explosion was an "embarrassment to China, which is trying to help but with little success."

..North Korea is a rogue nation which has become a great threat and embarrassment to China, which is trying to help but with little success.

"The United States is considering, in addition to other options, stopping all trade with any country doing business with North Korea," he later tweeted.

Act of defiance

While the test is a personal challenge to Trump it is also an act of defiance from Kim towards Beijing.

The detonation is also an unwelcome complication for China's President Xi Jinping, as he prepares for a crucial Communist Party National Congress, which is held every five years to chart the country's future policy path and leadership line up.

It is possible that the scale of defiance shown by Kim will force China's hand and convince it to move to a more hostile stance towards North Korea.

China did sign on to a tough new range of UN Security Council sanctions against Pyongyang which were passed in August in a major foreign policy success for the Trump administration. But US officials believe Xi could do far more to rein in Kim, given that his impoverished nation is dependent on China for energy supplies.

But China's end game in North Korea is not the same as Washington's. Its ultimate goal is to prevent a collapse of the regime in Pyongyang that could send millions of refugees into it's territory and destabilize communist rule.

It also wants to prevent the evolution of a unified Korea allied to the United States in a scenario that would change the strategic balance in northeast Asia.

One option for Washington is to signal that it is ready to impose comprehensive sanctions on Chinese firms that do business with the Pyongyang government, in an effort to force a tougher line than Beijing.

Still, there is no guarantee that strategy would work either, since Kim is showing every sign that he believes the survival of his regime is guaranteed by a deliverable nuclear arsenal and he is willing to do everything to achieve it.

Countries call for emergency UN Security Council meeting

The nuclear test — labeled by experts as the pariah state's most powerful ever — drew rebuke from around the globe, including from North Korea's strongest ally, with several nations joining forces to come up with an appropriate response.

The United States, Japan, France, the United Kingdom and South Korea quickly requested an emergency session of the UN Security Council after the test, which North Korea's leaders said demonstrated the country was capable of putting an advanced hydrogen bomb atop an intercontinental ballistic missile.

The meeting, now scheduled for Monday at 10 a.m. ET, was announced as UN Secretary-General António Guterres condemned the North Korean test as "profoundly destabilizing for regional security."

The power of the blast was not immediately clear. While the seismic tremors it created led a Norwegian group to say it was eight times more powerful than the bomb dropped on Hiroshima in 1945, South Korean experts said the yield was less than half the Norwegian group's estimate.